Monitored fermions with conserved $\mathrm{U}(1)$ charge
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912151507042304 |
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| author | Fava, Michele Piroli, Lorenzo Bernard, Denis Nahum, Adam |
| author_facet | Fava, Michele Piroli, Lorenzo Bernard, Denis Nahum, Adam |
| contents | We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$σ$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$σ$M and also discuss higher dimensional generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monitored fermions with conserved $\mathrm{U}(1)$ charge Fava, Michele Piroli, Lorenzo Bernard, Denis Nahum, Adam Statistical Mechanics Quantum Physics We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$σ$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$σ$M and also discuss higher dimensional generalizations. |
| title | Monitored fermions with conserved $\mathrm{U}(1)$ charge |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2407.08045 |